A Mathematician on Creativity, Art, Logic and Language(quantamagazine.org)
quantamagazine.org
A Mathematician on Creativity, Art, Logic and Language
https://www.quantamagazine.org/a-mathematician-on-creativity-art-logic-and-language-20240313/
21 comments
Context: I don't know much about Mirzakhani's work, but I'm a PhD student in algebraic geometry and I studied Hodge theory and complex manifolds.
> These smooth surfaces, not obviously connected to algebraic geometry
According to Wikipedia:
> Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".
But Riemann surfaces are the simplest complex manifolds, and the compact ones are algebraic curves. I don't see how the connection to algebraic geometry is "not obvious". Is there something deeper going on? I would like to learn a bit more :)
> These smooth surfaces, not obviously connected to algebraic geometry
According to Wikipedia:
> Mirzakhani was awarded the Fields Medal in 2014 for "her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces".
But Riemann surfaces are the simplest complex manifolds, and the compact ones are algebraic curves. I don't see how the connection to algebraic geometry is "not obvious". Is there something deeper going on? I would like to learn a bit more :)
Riemann surfaces are algebraic, but their moduli can mean two different things:
a) the (algebraic) moduli space of complex Riemann surfaces of a fixed genus (number of donut holes). This is an object in the realm of algebraic geometry in that it is possible to embed it into complex projective space, using for instance theta functions.
b) the moduli of complex structures on a fixed topological surface of genus g: this is Teichmuller space, which as far as we can tell only an object in differential geometry. However, Eskin, Mirzakhani, Filip and others have discovered that various subspaces of this non-algebraic space are 'naturally' algebraic (or more precisely quasi- projective). This is the surprising part.
a) the (algebraic) moduli space of complex Riemann surfaces of a fixed genus (number of donut holes). This is an object in the realm of algebraic geometry in that it is possible to embed it into complex projective space, using for instance theta functions.
b) the moduli of complex structures on a fixed topological surface of genus g: this is Teichmuller space, which as far as we can tell only an object in differential geometry. However, Eskin, Mirzakhani, Filip and others have discovered that various subspaces of this non-algebraic space are 'naturally' algebraic (or more precisely quasi- projective). This is the surprising part.
I wish I'd read "Is Maths Real" first before commenting here! Oh well...anyone with more insights? Sometimes I feel once the principles/axioms are laid out, a giant puzzle is untangled within that logical system, and I wonder how much is really practical math vs academic sandbox?
E.g. this quote "You need a new idea, a good definition, a statement that you think you’ll be able to exploit. Only then can your work start."
Why is such an idea necessary in the first place, is the context missing here?
"By learning about the objects, by manipulating them and using them in mathematical arguments, they ultimately become your friend."
E.g. this quote "You need a new idea, a good definition, a statement that you think you’ll be able to exploit. Only then can your work start."
Why is such an idea necessary in the first place, is the context missing here?
"By learning about the objects, by manipulating them and using them in mathematical arguments, they ultimately become your friend."
That math is sometimes practical is nice, but it's not the point.
I get the impression that mathematics really just is quantitative philosophy. I wonder what the etymology of math is.
it means "learning"
https://www.etymonline.com/word/*mendh-
https://www.etymonline.com/word/*mendh-
"A Mathematician"? It's Claire Voisin, not some rando... She's a huge deal. https://en.wikipedia.org/wiki/Claire_Voisin
Yeah. She was awarded the Crafoord prize this year, a distinction similar to the Nobel prize in other disciplines.
(Other mathematicians who were awarded the prize include Grothendieck, Deligne, Connes, Tao, Bombieri...).
The title is also weird. It's about her view on her (personal) ideas about maths, how she sees it, how it works for her. There are (almost) no statements about creativity, art, and language in general.
I think it has to do with her views on math being related to her other creative interests - saying you could compare a mathematical theorem to a poem, for example.
Also, where she talks about how she sits and works at a computer but that's not where the real work happens. The real work can happen when she's doing something that allows her mind to wander, like cleaning, but her mind is still working in the background.
Sounds like a creative process to me.
Also, where she talks about how she sits and works at a computer but that's not where the real work happens. The real work can happen when she's doing something that allows her mind to wander, like cleaning, but her mind is still working in the background.
Sounds like a creative process to me.
Nice article
Legend2440(3)
This person loves maths and art, and, we are told, is amazingly good at maths.
And yet, we see this pic:
https://d2r55xnwy6nx47.cloudfront.net/uploads/2024/03/Claire...
with this caption:
> Voisin sometimes relaxes by painting both original works (shown behind her) and copies of famous portraits, like the Amedeo Modigliani at bottom left.
She has colour co-ordinated pictures, with a material backdrop. This is then - badly - co-ordinated with the couch and its colours and patterns.
I'm genuinely surprised that this person's art choices and arrangements are so bad. She is meant to be a top tier mathematician + into art - so when these combine in her own life, can this really be the result?
I'm not critiquing her interior decor for the sake of being mean - I just find the example of art + reasoning that we see in the pic to be so inconsistent with the person that is being portrayed. Can this be how a top mathematician arranges things they love?
And yet, we see this pic:
https://d2r55xnwy6nx47.cloudfront.net/uploads/2024/03/Claire...
with this caption:
> Voisin sometimes relaxes by painting both original works (shown behind her) and copies of famous portraits, like the Amedeo Modigliani at bottom left.
She has colour co-ordinated pictures, with a material backdrop. This is then - badly - co-ordinated with the couch and its colours and patterns.
I'm genuinely surprised that this person's art choices and arrangements are so bad. She is meant to be a top tier mathematician + into art - so when these combine in her own life, can this really be the result?
I'm not critiquing her interior decor for the sake of being mean - I just find the example of art + reasoning that we see in the pic to be so inconsistent with the person that is being portrayed. Can this be how a top mathematician arranges things they love?
It seems entirely plausible that there wasn’t a good setting just emphasizing her and all her art for an article photo, and that paintings were temporarily moved to create one - in which case what you’re picking up on would represent the photographer and a compromise with expediency rather than the mathematician.
I think she likes flora.
Isn't that a common complaint from fine artists?
That their work must be dumbed down to fit into a coffee table book or match the colour coordination of some interior design?
Art appreciation has many dimensions, and arguably the most meaningful ones are the most personal and authentic, and do not require justification to other people.
That their work must be dumbed down to fit into a coffee table book or match the colour coordination of some interior design?
Art appreciation has many dimensions, and arguably the most meaningful ones are the most personal and authentic, and do not require justification to other people.
Yeah - its easy to explain and I'm not asking her for a justification.
I'm simply stating that here we are told is a top grade, highly-orderly brain with a great love of art, and artist herself - what a combination! And yet the arrangement of images and interior decoration is colour co-ordinated - and badly!
Its far from congruent with my expectations. The picture of the tree with misplaced branch is actually offensive to me - I would be getting rid of that picture.
I'm simply stating that here we are told is a top grade, highly-orderly brain with a great love of art, and artist herself - what a combination! And yet the arrangement of images and interior decoration is colour co-ordinated - and badly!
Its far from congruent with my expectations. The picture of the tree with misplaced branch is actually offensive to me - I would be getting rid of that picture.
The Hodge conjecture has a similar philosophy: you define certain data in terms of "harmonic analysis" on the geometric object, and the conjecture says that they all correspond to the algebraic data out of which the object can be rebuilt.